Finite Group Databasebeta

← #14645641

Subgroups — #14645641

Order 2816.

758 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13068426C211yesmaximal, characteristic, complemented
2#13067223C211yesmaximal, characteristic, complemented
3#13067124C211yesmaximal, characteristic, complemented
4#13067102C211yesmaximal, characteristic, complemented
5#13067050C211yesmaximal, characteristic, complemented
6#13067033C211yesmaximal, characteristic, complemented
7C11×#3517C211yesmaximal, characteristic
8C11×#557C411yescharacteristic, complemented
9C11×#553—22no—
10C11×#553—21no—
11C11×#550—21no—
12C11×#550—21no—
13C11×#550C411yescharacteristic, complemented
14C11×#550C411yescharacteristic, complemented
15C11×#547—21no—
16C11×#547C411yescharacteristic, complemented
17C11×#540—22no—
18C11×#540—21no—
19C11×#532—21no—
20C11×#532C2211yescharacteristic
21C11×#529—21no—
22C11×#529C2211yescharacteristic
23C11×#520—21no—
24C4×C11×#41C2211yescharacteristic
25C2×#66901—21no—
26#10622545C2211yescharacteristic
27#10622539C2211yescharacteristic
28#10622538C2211yescharacteristic
29C4×#4318C2211yescharacteristic
30#10622181—21no—
31#10622178—21no—
32#10622176—21no—
33#10622175—21no—
34#10622175—22no—
35Q8⋊(C11⋊C8)—21no—
36D4⋊(C11⋊C8)—22no—
37D4⋊(C11⋊C8)—21no—
38#10622170—21no—
39C2×C11×#41—21no—
40C2×C11×#41—21no—
41C2×C11×#41—21no—
42C2×C11×#41—21no—
43C2×C11×#41D411yescharacteristic
44C11×C4⋊Q8—21no—
45C11×C4⋊Q8C2×C411yescharacteristic
46C11×#127—22no—
47C11×#127—21no—
48C11×#127—21no—
49C11×#127C2×C411yescharacteristic
50C11×#126—22no—
51C11×#126—21no—
52C11×#125—22no—
53C11×#125—21no—
54C11×#125D411yescharacteristic
55C11×#124—21no—
56C11×#124D411yescharacteristic
57C11×#123—22no—
58C11×#123—22no—
59C11×#123—22no—
60C11×#123—21no—
61C11×#123—22no—
62C11×C22⋊Q8—21no—
63C11×C22⋊Q8D411yescharacteristic
64C11×#121—22no—
65C11×#121—22no—
66C11×#121—22no—
67C11×#121—22no—
68C11×#121—22no—
69C11×#121—21no—
70C11×#121—22no—
71C11×#121—22no—
72C11×#121—21no—
73C11×#121—21no—
74C11×#121—21no—
75C11×#121D411yescharacteristic
76C11×#121D412yes—
77C4×Q8×C11—21no—
78C4×Q8×C11—21no—
79C4×Q8×C11C2×C411yescharacteristic
80C4×Q8×C11C2×C411yescharacteristic
81C4×Q8×C11D411yescharacteristic
82C4×D4×C11—22no—
83C4×D4×C11—22no—
84C4×D4×C11—22no—
85C4×D4×C11—22no—
86C4×D4×C11—21no—
87C4×D4×C11—21no—
88C4×D4×C11—21no—
89C4×D4×C11—21no—
90C4×D4×C11—21no—
91C4×D4×C11—21no—
92C4×D4×C11C2×C411yescharacteristic
93C4×D4×C11C2×C411yescharacteristic
94C4×D4×C11D411yescharacteristic
95C4×D4×C11D412yes—
96C11×#117—22no—
97C11×#117—21no—
98C11×#117—21no—
99C11×#117D411yescharacteristic
100C2×C11×C4⋊C4—22no—
101C2×C11×C4⋊C4—21no—
102C2×C42×C11—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C4×Dic11—21no—
105C2×#4318—21no—
106#66901—24no—
107C11⋊#95—21no—
108C11⋊#95—21no—
109C22⋊(C11⋊C8)—21no—
110C22⋊(C11⋊C8)—21no—
111C4⋊(C11⋊C8)—21no—
112C4⋊(C11⋊C8)—21no—
113#66867—21no—
114#66867—21no—
115C4×C11⋊C8—21no—
116C4×C11⋊C8—21no—
117#8414—111nomaximal, Sylow
118C11×#41—22no—
119C11×#41—41no—
120C11×#41—42no—
121C11×#41—42no—
122C11×#41—82no—
123C11×#41—82no—
124C11×#41—82no—
125C2×Q8×C11—21no—
126C2×Q8×C11C22⋊C411yescharacteristic
127C2×Q8×C11C22⋊C411yescharacteristic
128C2×D4×C11—22no—
129C2×D4×C11—21no—
130C2×D4×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—22no—
133C2×D4×C11—22no—
134C2×D4×C11—21no—
135C2×D4×C11—22no—
136C2×D4×C11—21no—
137C2×D4×C11—21no—
138C2×D4×C11C22⋊C411yescharacteristic
139C2×D4×C11C22⋊C411yescharacteristic
140C2×D4×C11C22⋊C412yes—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—21no—
145C22×C4×C11—21no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×Dic11—41no—
153C11×C4⋊C4—22no—
154C11×C4⋊C4—22no—
155C11×C4⋊C4—22no—
156C11×C4⋊C4—22no—
157C11×C4⋊C4—21no—
158C11×C4⋊C4—21no—
159C11×C4⋊C4—21no—
160C11×C4⋊C4—21no—
161C11×C4⋊C4—21no—
162C11×C4⋊C4—21no—
163C11×C4⋊C4—21no—
164C11×C4⋊C4C22⋊C411yescharacteristic
165C11×C4⋊C4C22⋊C411yescharacteristic
166C11×C4⋊C4C22⋊C411yescharacteristic
167C11×C4⋊C4C22⋊C412yes—
168C11×C4⋊C4C22⋊C411yescharacteristic
169C11×C22⋊C4—22no—
170C11×C22⋊C4—22no—
171C11×C22⋊C4—22no—
172C11×C22⋊C4—21no—
173C11×C22⋊C4—21no—
174C11×C22⋊C4—21no—
175C11×C22⋊C4—21no—
176C11×C22⋊C4—21no—
177C11×C22⋊C4—21no—
178C11×C22⋊C4—22no—
179C11×C22⋊C4—21no—
180C11×C22⋊C4—21no—
181C11×C22⋊C4—22no—
182C42×C11—22no—
183C42×C11—21no—
184C42×C11—21no—
185C42×C11—21no—
186C42×C11—21no—
187C42×C11C22×C411yescharacteristic
188C42×C11C2×D411yescharacteristic
189C42×C11C2×D411yescharacteristic
190C42×C11C2×D411yescharacteristic
191C4×Dic11—22no—
192C4×Dic11—41no—
193#4318—22no—
194#4318—41no—
195C2×C11⋊C8—41no—
196C2×C11⋊C8—41no—
197C2×C11⋊C8—41no—
198#3517D1111yescharacteristic
199#1759—111no—
200#1529—111no—
201#1505—111no—
202#1500—111no—
203#1488—111no—
204#1484—111no—
205C23×C11—21no—
206C23×C11—22no—
207C23×C11—21no—
208C23×C11#12011yescharacteristic
209Q8×C11—21no—
210Q8×C11—41no—
211Q8×C11—42no—
212Q8×C11#10412yes—
213D4×C11—21no—
214D4×C11—21no—
215D4×C11—42no—
216D4×C11—42no—
217D4×C11—41no—
218D4×C11—44no—
219D4×C11—42no—
220D4×C11—41no—
221D4×C11—41no—
222D4×C11—81no—
223D4×C11—82no—
224D4×C11—82no—
225D4×C11—82no—
226D4×C11—82no—
227D4×C11—82no—
228C2×C4×C11—21no—
229C2×C4×C11—21no—
230C2×C4×C11—21no—
231C2×C4×C11—21no—
232C2×C4×C11—21no—
233C2×C4×C11—21no—
234C2×C4×C11—21no—
235C2×C4×C11—22no—
236C2×C4×C11—21no—
237C2×C4×C11—41no—
238C2×C4×C11—41no—
239C2×C4×C11—42no—
240C2×C4×C11—44no—
241C2×C4×C11—42no—
242C2×C4×C11—41no—
243C2×C4×C11—41no—
244C2×C4×C11—81no—
245C2×C4×C11—82no—
246C2×C4×C11—82no—
247C2×C4×C11—82no—
248C2×C4×C11C2×C22⋊C411yescharacteristic
249C2×C4×C11C2×C22⋊C411yescharacteristic
250C2×C4×C11C2×C22⋊C411yescharacteristic
251C2×C4×C11#12011yescharacteristic
252C2×C4×C11#12011yescharacteristic
253C2×C4×C11#12011yescharacteristic
254C2×Dic11—42no—
255C2×Dic11—81no—
256C2×Dic11—81no—
257C11⋊C8—42no—
258C11⋊C8—81no—
259C11⋊C8—81no—
260#557Dic1111yescharacteristic, complemented
261#553—22no—
262#553—21no—
263#550—21no—
264#550—21no—
265#550Dic1111yescharacteristic, complemented
266#550Dic1111yescharacteristic, complemented
267#547—21no—
268#547Dic1111yescharacteristic, complemented
269#540—22no—
270#540—21no—
271#532—21no—
272#532C2×D1111yescharacteristic
273#529—21no—
274#529C2×D1111yescharacteristic
275#520—21no—
276C4×#41C2×D1111yescharacteristic
277#432—111no—
278#431—111no—
279C2×#104—221no—
280C4×M16—111no—
281#376—111no—
282#339—221no—
283#330—221no—
284#329—221no—
285#328—221no—
286#327—221no—
287#327—222no—
288Q8⋊C8—221no—
289D4⋊C8—222no—
290D4⋊C8—221no—
291C22×C11—21no—
292C22×C11—21no—
293C22×C11—21no—
294C22×C11—41no—
295C22×C11—42no—
296C22×C11—41no—
297C22×C11—41no—
298C22×C11—42no—
299C22×C11—41no—
300C22×C11—41no—
301C22×C11—42no—
302C22×C11—41no—
303C22×C11#37911yescharacteristic
304C4×C11—21no—
305C4×C11—21no—
306C4×C11—21no—
307C4×C11—21no—
308C4×C11—21no—
309C4×C11—22no—
310C4×C11—41no—
311C4×C11—41no—
312C4×C11—41no—
313C4×C11—41no—
314C4×C11—42no—
315C4×C11—41no—
316C4×C11C2×#10411yescharacteristic
317C4×C11#42111yescharacteristic
318Dic11—82no—
319C2×#41—21no—
320C2×#41—21no—
321C2×#41—21no—
322C2×#41—21no—
323C2×#41C22⋊D1111yescharacteristic
324C2×M16—221no—
325C4⋊Q8—21no—
326C4⋊Q8C2×Dic1111yescharacteristic
327#127—22no—
328#127—21no—
329#127—21no—
330#127C2×Dic1111yescharacteristic
331#126—22no—
332#126—21no—
333#125—22no—
334#125—21no—
335#125C22⋊D1111yescharacteristic
336#124—21no—
337#124C22⋊D1111yescharacteristic
338#123—22no—
339#123—22no—
340#123—22no—
341#123—21no—
342#123—22no—
343C22⋊Q8—21no—
344C22⋊Q8C22⋊D1111yescharacteristic
345#121—22no—
346#121—22no—
347#121—22no—
348#121—22no—
349#121—22no—
350#121—21no—
351#121—22no—
352#121—22no—
353#121—21no—
354#121—21no—
355#121—21no—
356#121C22⋊D1111yescharacteristic
357#121C22⋊D1112yes—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8C2×Dic1111yescharacteristic
361C4×Q8C2×Dic1111yescharacteristic
362C4×Q8C22⋊D1111yescharacteristic
363C4×D4—22no—
364C4×D4—22no—
365C4×D4—22no—
366C4×D4—22no—
367C4×D4—21no—
368C4×D4—21no—
369C4×D4—21no—
370C4×D4—21no—
371C4×D4—21no—
372C4×D4—21no—
373C4×D4C2×Dic1111yescharacteristic
374C4×D4C2×Dic1111yescharacteristic
375C4×D4C22⋊D1111yescharacteristic
376C4×D4C22⋊D1112yes—
377#117—22no—
378#117—21no—
379#117—21no—
380#117C22⋊D1111yescharacteristic
381C2×C4⋊C4—22no—
382C2×C4⋊C4—21no—
383C2×C42—21no—
384C2×C42—221no—
385C2×C42C22×D1111yescharacteristic
386C4⋊C8—221no—
387C4⋊C8—221no—
388#104—224no—
389C22⋊C8—221no—
390C22⋊C8—221no—
391#97—221no—
392#97—221no—
393C4×C8—221no—
394C4×C8—221no—
395#95—221no—
396#95—221no—
397C2×C11—41no—
398C2×C11—81no—
399C2×C11—82no—
400C2×C11—81no—
401C2×C11#178911yescharacteristic
402C2×C11#179411yescharacteristic
403C2×C11#179511yescharacteristic
404#41—22no—
405#41—41no—
406#41—42no—
407#41—42no—
408#41—82no—
409#41—82no—
410#41—82no—
411C2×Q8—21no—
412C2×Q8C22⋊Dic1111yescharacteristic
413C2×Q8C22⋊Dic1111yescharacteristic
414C2×D4—22no—
415C2×D4—21no—
416C2×D4—22no—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—22no—
420C2×D4—21no—
421C2×D4—22no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4C22⋊Dic1111yescharacteristic
425C2×D4C22⋊Dic1111yescharacteristic
426C2×D4C22⋊Dic1112yes—
427C22×C4—22no—
428C22×C4—22no—
429C22×C4—22no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—441no—
436C22×C4C2×C22⋊D1111yescharacteristic
437C22×C4C2×C22⋊D1111yescharacteristic
438C22×C4C2×C22⋊D1111yescharacteristic
439M16—222no—
440M16—441no—
441C2×C8—441no—
442C2×C8—441no—
443C2×C8—441no—
444C4⋊C4—22no—
445C4⋊C4—22no—
446C4⋊C4—22no—
447C4⋊C4—22no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4C22⋊Dic1111yescharacteristic
456C4⋊C4C22⋊Dic1111yescharacteristic
457C4⋊C4C22⋊Dic1111yescharacteristic
458C4⋊C4C22⋊Dic1112yes—
459C4⋊C4C22⋊Dic1111yescharacteristic
460C22⋊C4—22no—
461C22⋊C4—22no—
462C22⋊C4—22no—
463C22⋊C4—21no—
464C22⋊C4—21no—
465C22⋊C4—21no—
466C22⋊C4—21no—
467C22⋊C4—21no—
468C22⋊C4—21no—
469C22⋊C4—22no—
470C22⋊C4—21no—
471C22⋊C4—21no—
472C22⋊C4—22no—
473C42—22no—
474C42—21no—
475C42—21no—
476C42—21no—
477C42—21no—
478C42—222no—
479C42—441no—
480C42C22×Dic1111yescharacteristic
481C42C2×C22⋊D1111yescharacteristic
482C42C2×C22⋊D1111yescharacteristic
483C42C2×C22⋊D1111yescharacteristic
484C11#841411yescharacteristic, complemented, Sylow
485C23—21no—
486C23—22no—
487C23—21no—
488C23#6700611yescharacteristic
489Q8—21no—
490Q8—41no—
491Q8—42no—
492Q8#6690112yes—
493D4—21no—
494D4—21no—
495D4—42no—
496D4—42no—
497D4—41no—
498D4—44no—
499D4—42no—
500D4—41no—
501D4—41no—
502D4—81no—
503D4—82no—
504D4—82no—
505D4—82no—
506D4—82no—
507D4—82no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—22no—
516C2×C4—21no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—42no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—81no—
525C2×C4—82no—
526C2×C4—82no—
527C2×C4—82no—
528C2×C4—442no—
529C2×C4—881no—
530C2×C4—881no—
531C2×C4C2×C22⋊Dic1111yescharacteristic
532C2×C4C2×C22⋊Dic1111yescharacteristic
533C2×C4C2×C22⋊Dic1111yescharacteristic
534C2×C4#6700611yescharacteristic
535C2×C4#6700611yescharacteristic
536C2×C4#6700611yescharacteristic
537C8—442no—
538C8—881no—
539C8—881no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—41no—
544C22—42no—
545C22—41no—
546C22—41no—
547C22—42no—
548C22—41no—
549C22—41no—
550C22—42no—
551C22—41no—
552C22#1062286011yescharacteristic
553C4—21no—
554C4—22no—
555C4—21no—
556C4—21no—
557C4—21no—
558C4—21no—
559C4—41no—
560C4—41no—
561C4—41no—
562C4—41no—
563C4—42no—
564C4—41no—
565C4—882no—
566C4C2×#6690111yescharacteristic
567C4#1062284911yescharacteristic
568C2—41no—
569C2—81no—
570C2—82no—
571C2—81no—
572C2#1306856011yescharacteristic
573C2#1306858011yescharacteristic
574C2#1306858611yescharacteristic
subgroupG/H
centerC22#10622860
commutatorC42×C11C22×C4
FrattiniC2×C42C22×D11
Fitting, prime radicalC11×#3517C2
socleC22×C11#379
cosocleC2×C42×C11C23
hypercenter#3517D11
hypocenterC11#8414
LCSG ▷ C42×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3517

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #13068426C2semidirect
2. #13067223C2semidirect
3. #13067124C2semidirect
4. #13067102C2semidirect
5. #13067050C2semidirect
6. #13067033C2semidirect
8. C11×#557C4semidirect
13. C11×#550C4semidirect
14. C11×#550C4semidirect
16. C11×#547C4semidirect
260. #557Dic11semidirect
265. #550Dic11semidirect
266. #550Dic11semidirect
268. #547Dic11semidirect
484. C11#8414semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130684262
#130672232
#130671242
#130671022
#130670502
#130670332
C11×#35172
#841411